What is Kaprekar's Constant?

Named after the Indian mathematician D. R. Kaprekar, the number 6174 is known as Kaprekar's Constant. Kaprekar found that by recursively sorting and subtracting four-digit numbers, solutions will converge upon the number 6174.

Performing Kaprekar's Routine

The algorithm is as follows:

  1. Take any four-digit number, using at least two distinct digits (leading zeros are allowed).
  2. Arrange the digits in both descending and ascending order to get two four digit numbers, adding leading zeros if necessary.
  3. Subtract the smaller number from the bigger number.
  4. If the result is not 6174, go back to step 2 and repeat this process.

The only four-digit numbers for which Kaprekar's routine does not reach 6174 are: 0000, 1111, 2222, 3333, 4444, 5555, 6666, 7777, 8888, 9999.

Example:

Starting with the number 8991:

  • 9981 - 1899 = 8082
  • 8820 - 0288 = 8532
  • 8532 - 2358 = 6174

Running Kaprekar's Routine

This repository contains a script for running Kaprekar's routine. Usage is as follows:

kaprekar.routine( number );

This function will return an object with the number of iterations and steps used in the routine.